According to an astronomy club, Earth is a plane described by the equation
x + y + z = 18.

The club also stated that Earth will be destroyed by an explosion that will spontaneously occur at point A = (1, 1, 1). Note that point A is not a point on Earth, it is a point in space that will explode and will impact Earth.

a/ Calculate the co-ordinate of the first point that is going to be destroyed by this explosion.

b/ What is the distance between point A and the first point that is going to be destroyed (mentioned in a)? (Hint: Shortest Distance)

April 16th 2010, 06:07 PM

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Quote:

Originally Posted by shiiganB

According to an astronomy club, Earth is a plane described by the equation
x + y + z = 18.

The club also stated that Earth will be destroyed by an explosion that will spontaneously occur at point A = (1, 1, 1). Note that point A is not a point on Earth, it is a point in space that will explode and will impact Earth.

a/ Calculate the co-ordinate of the first point that is going to be destroyed by this explosion.

b/ What is the distance between point A and the first point that is going to be destroyed (mentioned in a)? (Hint: Shortest Distance)

We want to find the line perpendicular to the plane passing through the point; this will tell us the minimal distance between the point and the plane.

For a plane , we have normal vector .

The vector equation of the line passing through point with direction vector is

In this case, write

This can also be written

In other words, we have a parametric equation described by

Combine with to get

So the point that gets hit first is , and to find the distance, use the Pythagorean theorem (generalized for three dimensions):

Note that the line we found earlier also passes through the origin, so it could be expressed more concisely as